This article is cited in 3 papers

RESEARCH ARTICLE

Some commutativity criteria for $3$-prime near rings

A. Raji

LMACS Laboratory, Faculty of Sciences and Technology, Sultan Moulay Slimane University, P.O.Box 523, 23000, Beni Mellal, Morocco

Abstract: In the present paper, we introduce the notion of $*$-generalized derivation in near-ring $N$ and investigate some properties involving that of $*$-generalized derivation of a $*$-prime near-ring $N$ which forces $N$ to be a commutative ring. Some properties of generalized semiderivations have also been given in the context of $3$-prime near-rings. Consequently, some well known results have been generalized. Furthermore, we will give examples to demonstrate that the restrictions imposed on the hypothesis of various results are not superfluous.

Keywords: $3$-prime near-rings, $3$-semiprime near-rings, involution, $*$-derivation, semiderivation, commutativity.

MSC: 16N60, 16W25, 16Y30

Received: 18.08.2019
Revised: 26.04.2021

Language: English

DOI: 10.12958/adm1439